Question

Ex. 18,19. Urgent. Va rog.

Answer 1

18. Determinati x∈N*, astfel incat fractiile urmatoare sa fie subunitare:
a)  5/x    x>5     x={6, 7, 8, .........+∞}
b) 10/(x+1)     x+1>10/-1   x>9     x={10, 11, 12, 13, ..........., +∞}
c)  7/(4x-13)    4x-13>7 /+13   4x>20 /:4    x>5     x={6, 6, 8, .........,}
d)  (5x+2)/(x+30)   5x+2<x+30 /-x-2   4x<28 /:4    x<7    x={1, 2, 3, 4, 5, 6}
e)  (3x-5)/(x+15)    3x-5<x+15 /-x+5   2x<20 /:2     x<10   x={1, 2, 3, ...., 9}
f)  x²<100   x<√100     x<10     x={1, 2, 3, ......., 9}.

19. Determinati x∈N*, astfel incat fractiile urmatoare sa fie supraunitare.
a) 5/x   x<5      x={1, 2, 3, 4}
b) 10/(x+1)   x+1<10 /-1  x<9    x={1, 2, 3, 4, 5, 6, 7}
c) 7/(4x-13)   4x-13<7 /+13   4x<20/:4  x<5   x={1, 2, 3, 4}
d) (5x+2)/(x+30)   5x+2>x+30/-x-2  4x>28/:4  x>7   x={8, 9, 10,..........+∞}
e) x²/100   x²>100    x>√100    x>10    x={11, 12, 13, 14, ..........+∞}
f) 49/(x+1)²   (x+1)²<49   x+1<√49   x+1<7/-1   x<6     x={1, 2, 3, 4, 5}